Jeżeli zajrzysz do słownika ,,diki" i wpiszesz słówko concerned to w punkcie 2. masz napisane " synonim: anxious". To chyba wszystko wyjaśnia.

Dokładnie tak, anxious i concerned są synonimami i możemy ich używać zamiennie.

Moim zdaniem, 'anxious' jest nieco silniejsze niz 'concerned', gdyz pochodzi od 'lek - anxiety' i jest uzywane w zargonie psychiatryczno-psychologicznym, jako np. jeden z objawow nerwicy. 'To be concerned about something' oznacza martwic sie o cos, ale tez byc czyms po prostu zainteresowanym; 'anxious' bez dwoch zdan wskazuje na stres.

do Megan273: dobrze zauważone; w słowniku diki właśnie wychwyciłam tą różnicę w tłumaczeniu:
anxiety-niepokój, obawa, lęk
concern-niepokój, obawa, troska
:D

Hejka

Bardzo dobre wyjaśnienie różnic pomiędzy tymi wyrazami podaje OALD.

worried/concerned/nervous/anxious/uneasy

These words all describe feeling unhappy and afraid because you are thinking about unpleasant things that might happen or might have happened. 
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worried

thinking about unpleasant things that might happen or might have happened and therefore feeling unhappy and afraid 
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concerned

worried and feeling concern about sth
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worried or concerned?

Concerned is usually used when you are talking about a problem that affects another person, society, the world, etc, while worried can be used for this or for more personal matters. 
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nervous -> feeling worried about sth or slightly afraid of sth 
anxious -> feeling worried or nervous about sth
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worried, nervous or anxious?

Worried is the most frequent word to describe how you feel when you are thinking about a problem or something bad that might happen.

Anxious can describe a stronger feeling and is more formal.

Nervous is more often used to describe how you feel before you do something very important such as an exam or an interview, or something unpleasant or difficult.

Nervous can describe sb's personality: a very nervous girl is often or usually nervous; a worried girl is worried on a particular occasion or about a particular thing.

Worried describes her feelings, not her personality.
Anxious may describe feelings or personality. 

uneasy -> feeling worried or unhappy about a particular situation, especially because you think sth bad may happen or because you are not sure that what you are doing is right

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